Projective Structures on Curves and Conformal Geometry

Florin Belgun () and Andrei Moroianu ()
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Florin Belgun: Institute of Mathematics “Simion Stoilow” of the Romanian Academy
Andrei Moroianu: Laboratoire de mathématiques d’Orsay, Université Paris-Saclay, CNRS

A chapter in Real and Complex Geometry, 2025, pp 41-73 from Springer

Abstract: Abstract Projective structures on curves appear naturally in many areas of mathematics, from extrinsic conformal geometry to analysis, where the main problem is to find qualitative information about the solutions of Hill equations. In this paper, we describe in detail the correspondence between different equivalent definitions of projective structures and their isomorphism classes, correcting long-standing inexactitudes in the literature. As an application, we show that the Yamabe problem for curves in a conformal/Möbius ambient space has no solutions in general.

Keywords: Conformal structure; Projective structure; Laplace structure; Möbius structure; Primary 53A20; 53A30; 53A55 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_2

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DOI: 10.1007/978-3-031-92297-8_2

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